Question

Find the number of $5$-digit odd numbers that can be formed using the integers from $3$ to $9$ if no digit is to occur more than once in any number

• A. $1440$
• B. $180$
• C. $360$
• D. $720$

Answer 1

The correct option is A $1440$

The digits from which we can choose digits is $3,4,5,6,7,8,9$, that is a total of $7$ digits
Since each desired number has to be odd , so we must have any of $3,5,7,9$ at the units place. This can be done in $4$ ways
Then ten thousands, thousands, hundreds, and tens place can be filled up by remaining $6$ digits in ${}^6{P}_4=\frac{6!}{(6-4)!}=\frac{6!}{2!}=6\times 5\times 4\times 3=360$ ways
So, total number of $5$ digit odd numbers that can be formed $=360\times 4=1440$